
Local learning method (LLM) is defined as the algorithm utilized by each client \(C_{i}\)  over the local dataset \(D_{C_i}\)  to obtain the underlying causal structure \(G_{C_i} = (X, E_{C_i})\) . As discussed in sec:preliminaries, we currently support both ENCO [1]} and SDI [2]} as LLMs, but the set of methods could potentially expand to incorporate other continuous-optimization based methods as well.

Belief matrix (\(\tilde{\sigma }\) ) has the same dimensions as the adjacency matrix of \(G\)  but each element represents an existence belief, denoted by \(\tilde{\sigma }_{i,j} \in [0, 1]\)  between \(X_i\)  and \(X_j\) , where a value close to 1 indicates high possibility of a direct link between \(X_i\)  and \(X_j\) .

